Cutaway applique allows you to transform regular turned applique into a sort of patchwork. That is removing the buildup of layers and leaving you with a seemingly pieced cloth. A great way to get curves into your work without piecing curved seams which is difficult for some.
Here is an example from Small Journeys, One of the free tutorial series I offer here.
Here is a link to the Small Journeys post if you wish to follow that thread.